A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4# and the angle between sides B and C is #pi/6#. If side B has a length of 8, what is the area of the triangle?

1 Answer
sankarankalyanam
Mar 27, 2018

#color(green)(Delta " " A_t = (1/2) a b sin C = 11.71 " sq units"#

Explanation:

#hat A = pi/6, hat C = pi/4, b = 8#

#hat B = pi - pi/6 - pi/4 = (7pi)/12#

Applying the Law of Sines,

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/](useruploads.socratic.org)

#a = (b sin A) / sin B = (8 * sin (pi/6) ) / sin ((7pi)/12) = 4.14 " units"#

#color(green)(Delta " " A_t = (1/2) a b sin C = (1/2) * 4.14 * 8 * sin (pi/4) = 11.71 " sq units"#

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